[1]} is credited as the first to prove the equivalence of the ROC-AUC and the Mann-Whitney test statistic [2]}.
This equivalence has led many authors to propose algorithms based on loss functions that are convex surrogates of the Mann-Whitney statistic.
[3]} proposed a global approximation of AUC which was then used in several other algorithms.
For example, [4]} used that approxmation to propose the AUCtron algorithm which learns a linear model.
[5]} proposed a quadratic time support vector machine algorithm for AUC maximization based on a pairwise loss function, and
[6]} proposed a similar approach based on boosting.
[7]} extended this approach to the partial AUC, which is defined as the area under the curve between two false positive rates (not necessarily 0 and 1).
[8]} analyze how much risk and regret is increased for balanced margin-based losses, compared with pairwise losses.
[9]} showed that in some cases margin-based losses yield the same solution as a pairwise loss.
For stochastic optimization of the AUC, [10]} proposed solving a saddle point problem involving a pairwise square loss, and
[11]} proposed to extend this approach to the squared hinge loss.
